Question

In: Operations Management

CC Car Wash specializes in car cleaning services. The services offered by the company, the exact...

  1. CC Car Wash specializes in car cleaning services. The services offered by the company, the exact service time, and the resources needed for each of them are described in the table following:

    Service

    Description

    Processing Time

    Resource

    A. Wash

    Exterior car washing and drying

    10 minutes

    1 automated washing machine

    B. Wax

    Exterior car waxing

    15 minutes

    1 automated waxing machine

    C. Wheel Cleaning

    Detailed cleaning of all wheels

    16 minutes

    1 employee

    D. Interior Cleaning

    Detailed cleaning inside the car

    20 minutes

    1 employee

    The company offers the following packages to their customers:

    • Package 1: Includes only car wash (service A).

    • Package 2: Includes car wash and waxing (services A and B).

    • Package 3: Car wash, waxing, and wheel cleaning (services A, B, and C).

    • Package 4: All four services (A, B, C, and D).

    Customers of CC Car Wash visit the station at a constant rate (you can ignore any effects of variability) of 50 customers per day. Of these customers, 30 percent buy Package 1, 30 percent buy Package 2, 15 percent buy Package 3, and 25 percent buy Package 4. The mix does not change over the course of the day. The store operates 10 hours a day.

    f. What is the implied utilization rate for the employee at service C (wheel cleaning)? Round your answer to the nearest whole number and ignore the percentage sign. For example, if your answer is 0.45 or 45%, fill in 45; if your answer is 0.76 or 76%, fill in 76.

    Your answer is .

Solutions

Expert Solution

Demand rate per package:

Total arrival rate per day = 50 customers

Package type

% of arrival

Demand rate per day

P1

0.3

50*0.3

= 15

p2

0.3

50*0.3

= 15

p3

0.15

50*0.15

= 7.5

P4

0.25

12.5

Demand rate at the workstations:

A

B

C

D

P1 (15)

P2 (15)

P2 (15)

P3 (7.5)

P3 (7.5)

P3 (7.5)

P4 (12.5)

P4 (12.5)

P4 (12.5)

P4 (12.5)

Total Demand per day

50

35

20

12.5

Determine flow rate and capacity of the workstation:

Workstation

A

B

C

D

Processing time per unit (p)

10

15

16

20

Resources (r)

1

1

1

1

Capacity/hr

= (60/p) x r

60/10*1

= 6

4

3.75

3

Capacity/day

= capacity/hr x 10 hours per day

6*10

= 60

40

37.5

30

Demand rate per day

50

35

20

12.5

flow rate

= minimum (demand rate, capacity)

=min(60, 50)

= 50

35

20

12.5

Utilization

= Flow rate / capacity x 100

50/60 x 100

= 83%

88%

53%

42%

Utilization of the workstation C = 53%


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